Marc Leonetti

3D vesicle dynamics simulations with a linearly triangulated surface

Simulations of biomembranes have gained an increasing interest in the past years. Specificities of these membranes propose new challenges for the numerics. In particular, vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint. A method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described. This method is coupled with a boundary element method solver for inner and outer fluids, to compute vesicle dynamics under external flows. The surface incompressibility constraint is satisfied by the construction of a projection operator.

Axisymmetric Boundary Element Method for vesicles in a capillary

The problem of a vesicle transported by a fluid flow can present a large range of length scales. One example is the case of a vesicle producing a tether, and eventually pearls, in an elongational flow. Another case occurs when a lubrication film is formed, such as during the short range interaction between two vesicles. Such problems are still challenging for 3D simulations. On the other hand, a good understanding could be obtained by first considering the axisymmetric regime when such a regime exists. An axisymmetric model could then be used, without the criticisms that can be made of a 2D approach. We propose such a model, primarily interested in flows through narrow cylindrical capillaries. Two options are compared, with and without explicit representation of the capillary boundaries by a mesh. The numerical effort is characterized as a function of the vesicles initial shape, the flow magnitude and the confinement. The model is able to treat typical configurations of red blood cells flowing through very narrow pores with extremely thin lubrication films.

Characterization of the mechanical properties of cross-linked serum albumin microcapsules: effect of size and protein concentration

A microfluidic technique is used to characterize the mechanical behavior of capsules that are produced in a two-step process: first, an emulsification step to form droplets, followed by a cross-linking step to encapsulate the droplets within a thin membrane composed of cross-linked proteins. The objective is to study the influence of the capsule size and protein concentration on the membrane mechanical properties. The microcapsules are fabricated by cross-linking of human serum albumin (HSA) with concentrations from 15 to 35 % (w/v). A wide range of capsule radii (∼40–450 μm) is obtained by varying the stirring speed in the emulsification step. For each stirring speed, a low threshold value in protein concentration is found, below which no coherent capsules could be produced. The smaller the stirring speed, the lower the concentration can be. Increasing the concentration from the threshold value and considering capsules of a given size, we show that the surface shear modulus of the membrane increases with the concentration following a sigmoidal curve. The increase in mechanical resistance reveals a higher degree of cross-linking in the membrane. Varying the stirring speed, we find that the surface shear modulus strongly increases with the capsule radius: its increase is two orders of magnitude larger than the increase in size for the capsules under consideration. It demonstrates that the cross-linking reaction is a function of the emulsion size distribution and that capsules produced in batch through emulsification processes inherently have a distribution in mechanical resistance.

Cotransport-induced instability of membrane voltage in tip-growing cells.

A salient feature of stationary patterns in tip-growing cells is the key role played by the symports and antiports, membrane proteins that translocate two ionic species at the same time. It is shown that these cotransporters destabilize generically the membrane voltage if the two translocated ions diffuse differently and carry a charge of opposite (same) sign for symports (antiports). The orders of magnitude obtained for the time and length scale are in agreement with experiments. A weakly nonlinear analysis characterizes the bifurcation.

One-step preparation of surface modified electrospun microfibers as suitable supports for protein immobilization

We have here developed a straightforward one-step route to surface modified polystyrene (PS) based microfibers for protein/enzyme immobilization. Our approach consists of wet electrospinning of a poly(styrene-alt-maleic anhydride) (PSMA) polymer in an aqueous solution collector which contains the (macro)molecules to be coupled, here PEG diamine (PEGDA) or hexamethylene diamine (hexDA). The amino groups on the fiber surface were then exploited for immobilization of the horseradish peroxidase (HRP) enzyme. The immobilized HRP amounts were higher on the PEG- and hexyl-modified fibers than on the non-modified PSMA ones. The HRP catalytic activity was evaluated with 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) as a substrate. While the retained activity of the enzyme immobilized on unmodified PSMA microfibers was only 2.4% of free enzyme, that of the enzyme immobilized on the PEGylated fibers increased to 34%. As a comparison, HRP fixed on hexyl-functionalized fibers exhibited a retention activity of 19.7%, showing the impact of a PEG spacer on HRP activity. HRP immobilization on PEG and hexyl-coated fibers had also a beneficial impact on enzyme storage stability. This study highlights the impact of surface properties on the activity of the immobilized enzyme and provides a convenient route to simultaneous elaboration/modification of fibers, for suitable protein fixation.

Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow

We develop an algorithm for the three dimensional simulation of the dynamics of soft objects (drops, capsules, vesicles) under creeping flow conditions. Loop elements are used to describe the shape of the soft objects. This surface representation is used both for membrane solver based on finite element method (FEM) and for the fluid solver based on the boundary element method (BEM). This isogeometric analysis of the low Reynolds fluidstructure interaction problem is then coupled to high-order explicit time stepping or second-order implicit time stepping algorithm. For vesicles simulation, a preconditioner is designed for the resolution of the surface velocity incompressibility constraint, which is treated by the use of a local Lagrange multiplier. A mesh quality preserving algorithm is introduced to improve the control mesh quality over long simulation times. We test the proposed algorithm on capsule and vesicle dynamics in various flows, and study its convergence properties, showing a second-order convergence O(N2) with mesh number of elements.

Plant VDAC Permeability: Molecular Basis and Role in Oxidative Stress

The mitochondrial voltage-dependent anion-selective channel (VDAC) is highly abundant in the mitochondrial outer membrane. It is permeable to molecules with a size up to about 5 kDa and is the main pathway for the exchange of metabolites and ions between the mitochondrial intermembrane space and the cytosol. Experimental studies performed for plant VDAC have shown that the channel displays properties reported for VDACs of other eukaryotic organisms. Firstly, it transports compounds as diverse as inorganic ions (e.g., K+ and Cl−), adenylates (e.g., ATP and AMP), and large macromolecules (tRNA and DNA). Secondly, despite its wide pore, the channel displays selectivity toward these compounds, i.e., it distinguishes between K+ and Cl− but also between ATP and AMP. The question of how VDAC can selectively transport these different compounds is addressed in this chapter based on data obtained for plant VDAC. It is well known that all organisms have at least one canonical VDAC isoform that shares similar electrophysiological properties and secondary structure with cognate VDAC of other organisms. For instance, this is the case of the mammalian VDAC1, the yeast Saccharomyces cerevisiae VDAC1 and the PcVDAC purified from the bean Phaseolus coccineus seeds. Consequently, Brownian dynamic simulations of monatomic ion permeation through the experimental three-dimensional structure of the mammalian VDAC1 and the PcVDAC modeled structure predict fairly well conductance and selectivity of both proteins. In addition, the data of molecular simulation studies performed on the mammalian VDAC1 agree with the experimental data obtained for PcVDAC, which suggests a similar permeation process for these VDAC proteins. Accordingly, both the experimental and theoretical studies indicate that the selectivity for inorganic ions is a consequence of the excess of positive charges and their distribution inside the pore and the absence of defined pathways for the permeation. In contrast, the permeation of metabolites involves a major binding site located at the N-terminal helix which folded into the pore lumen and occurs through a preferential pathway. The key residues forming the binding site are conserved in the PcVDAC pointing to the conserved permeation process. The process might be affected by VDAC interaction with other proteins. For example, it is suggested that plant VDAC is involved in the oxidative stress response which includes cytosolic hexokinase and thioredoxin binding to VDAC. This in turn may influence the exchange of molecules between the mitochondria and the cytosol.

The mitochondrial VDAC of bean seeds recruits phosphatidylethanolamine lipids for its proper functioning

The voltage-dependent anion-selective channel (VDAC) is the main pathway for inorganic ions and metabolites through the mitochondrial outer membrane. Studies recently demonstrated that membrane lipids regulate its function. It remains, however, unclear how this regulation takes place. In this study, we show that phospholipids are key regulators of Phaseolus VDAC function and, furthermore, that the salt concentration modulates this regulation. Both selectivity and voltage dependence of Phaseolus VDAC are very sensitive to a change in the lipid polar head from PC to PE. Interestingly enough, this dependence is observed only at low salt concentration. Furthermore, significant changes in VDAC functional properties also occur with the gradual methylation of the PE group pointing to the role of subtle chemical variations in the lipid head group. The dependence of PcVDAC gating upon the introduction of a small mole fraction of PE in a PC bilayer has prompted us to propose the existence of a specific interaction site for PE on the outer surface of PcVDAC. Eventually, comparative modeling and molecular dynamics simulations suggest a potential mechanism to get insight into the anion selectivity enhancement of PcVDAC observed in PE relative to PC.

Breathing instability in biological cells, patterns of membrane proteins

The activity of biological cells involves often the electric activity of its membranes which exhibit various spatiotemporal dynamics, from pulse, oscillatory bifurcation to stationary spatial modulation. This last kind of patterns appears on a typical diffusive time. A model has been proposed implying a coupling between the current flowing through membrane proteins and their electrophoretic motions in the case of mobile proteins. Here, we study the stability of the pattern in a 2D circular model cell versus the appearance of standing waves, the so-called breathing secondary instability.